Chopper-stabilized square cells

ABSTRACT

An RMS-DC converter includes a chopper-stabilized square cell that eliminates offset, thus enabling high-bandwidth operation. The chopper-stabilized offset requires only a small portion of the circuitry (i.e., a single component square cell) which operates at high frequencies, and is amenable to using high-bandwidth component square cells. Using the chopping technique minimizes required device sizes without compromising an acceptable square cell dynamic range, thereby maximizing the square cell bandwidth. The RMS-DC converter consumes less power than conventional RMS-to-DC converters that requires a high-frequency variable gain amplifier.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of U.S. patentapplication (“Co-pending patent application”), Ser. No. 14/092,131,entitled “High-Frequency RMS-DC Converter Using Chopper-StabilizedSquare Cells,” filed on Nov. 27, 2013 and relates to and claims priorityof U.S. provisional patent application (“Co-pending Provisional PatentApplication”), Ser. No. 61/767,628, entitled “High-Frequency RMS-DCConverter Using Chopper-Stabilized Square Cells,” filed on Feb. 21,2013. The disclosure of the copending patent applications are herebyincorporated by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to radio transmitter systems. Moreparticularly, the present invention relates to Root-Mean-Square (RMS) toDC converters, also called “RMS power detectors.”

2. Discussion of the Related Art

RMS power detectors typically operate within a dynamic range at a widerange of radio frequencies, thus RMS power detectors are found innumerous kinds of communication and instrumentation equipment, withspecial application in accurate measurements of average power levels ofsignals over time, independently of signal composition or “wave shape”.

One design challenge for RMS power detectors is to provide a sufficientdynamic range at high input frequencies, as measured by, for example, aratio of the largest input power level to the smallest input power levelthat can be accurately detected. Typically, the useable dynamic range ofan RMS-DC converter decreases as the input frequency increases. Thistradeoff is generally determined by the “square cell”, which is acircuit block that calculates the square of its input signal (i.e. theproduct of the input signal with itself). Many different square cellstructures are known in the literature (see, e.g., U.S. Pat. Nos.7,622,981, 5,489,868, 5,581,211, 6,549,057 and 7,342,431; see, also, thearticle “A 2 GHz mean-square power detector with integrated offsetchopper” (“Kouwenhoven”) by M. Kouwenhoven et al., published in Digestof Technical Papers, ISSCC 2005, pp. 124-125, February 2005). Althoughmost square cells have a high bandwidth, most have a poor dynamic rangebecause of DC offsets resulting from device mismatches. To achieve auseful dynamic range, many RMS-DC converters are enhanced by dynamicrange enhancement techniques. However, such dynamic range enhancementtechniques often significantly reduce the maximum operating frequency ofthe RMS power detector. The highest frequency achieved by RMS powerdetectors currently available on the market is typically not greaterthan 10 GHz, with a useable dynamic range of about 30 dB at thatfrequency. The maximum operating frequency does not scale well with thetransition or cut-off frequency (f_(T)) of a bipolar device, which isused in practically all RF RMS power detectors. The transit time ofminority carriers through the base does not determine the bandwidth ofthe square cell. Specifically, the square cell bandwidth is determinedby the base resistance and base-emitter junction capacitance.

Most square cell operations are based on the exponential relation in abipolar transistor between the collector current and the base-emittervoltage. Alternatively, in the few MOS¹-based examples, square celloperations may be based on the quadratic relation between the draincurrent and the gate-source voltage in an MOS device.Metal-Oxide-Semiconductor

The dynamic range of an RMS power detector is primarily limited by theDC offset resulting from mismatches between the bipolar or MOS devicesused in the RMS power detector. The bandwidth of an RMS power detectoris generally large, limited by junction capacitances, together with theimpedance of the voltage source driving the cell. Other methods forrealizing a squaring or root-mean-square function include using ananalog multiplier as the square cell (see, e.g., Kouwenhoven) or usingtrans-linear circuit techniques, such as those disclosed in U.S. Pat.No. 7,002,394. The bandwidth of a circuit using any of these techniquesis generally lesser than those of other types of square cells, while itsdynamic range is similar. Enlarging the devices, though a proventechnique to reduce the effects of device offsets, is not effective inenhancing the dynamic range of a square cell. For example, even doublingthe device sizes, the resulting offset may be reduced by merely a factorof √2, and thereby improves the output dynamic range by only 3 dB, whilethe bandwidth is reduced by a factor 2. As a result, due to thequadratic nature of the square cell, the input dynamic range is improvedonly by 1.5 dB. A dynamic range extension by 9 dB would require thedevices to be scaled up by a factor of 64, thereby reducing thebandwidth significantly.

Trimming is another alternative approach to reduce offsets withoutincreasing device sizes. In a square cell, trimming allows a higherbandwidth for a given dynamic range. Trimming, however, cannot removeall offset components from the square cell output signal (see, e.g.,Kouwenhoven). Especially over the full operating temperature range theeffectiveness of trimming is limited. Large device sizes are required tosuppress the remaining offset components.

The prior art relies significantly on increasing device sizes to improvethe square-cell dynamic range, at the expense of a reduced bandwidth ofthe square cell. However, device scaling cannot achieve both highbandwidth and a sufficiently wide dynamic range. Numerous circuittechniques may be used to increase the dynamic range of a square cellthat is suitable for use in a high dynamic range RMS-DC converter,although most of these techniques limit the attainable RMS detectorbandwidth.

As the dynamic range of an output signal of a square cell is muchgreater than the dynamic range of its input signal (typically at leasttwo times in dB), both small offsets and noise components in the outputsignal path can significantly reduce the overall dynamic range of an RMSpower detector. One method to increase the dynamic range of an RMS powerdetector is to compress the dynamic range of the square cell outputsignal, using a circuit with a non-linear transfer function. Forexample, U.S. Pat. No. 7,342,431 discloses a square cell followed by aDC LOG-amp. Such an approach has the advantage that only the square celloperates at high frequencies, while the rest of the circuitry is DC,thus enabling high-frequency operation, in principle. The disadvantagesof such an approach includes (a) the effect of an offset generatedinside the square cell on the dynamic range of the RMS power detector isnot mitigated (i.e., to achieve a reasonable dynamic range, largedevices and offset trimming are still required); (b) the attainablebandwidth is still significantly limited by the required large devicesizes; and (c) temperature drift and frequency dependence of the squarecell transfer function are directly observable in the overall detectortransfer function.

Other RMS-DC converters extend the dynamic range of an RMS powerdetector by placing a variable gain amplifier (VGA) at the inputterminal of a square cell, as depicted in FIG. 1. As shown in FIG. 1,input signal 101 is provided to VGA 102, which gain is controlled by VGAgain control circuit 105 based on output signal 104, in such a way thatthe magnitude of input signal 108 of square cell 107 is keptsubstantially constant over the full input power dynamic range of RMSpower detector 100. Low pass filter 106 removes the unwanted highfrequency components from the output signal of the square cell and RMSpower detector 100. The impact of any offset voltage in square cell 107is significantly reduced, since output signal 104 is much larger thanthe offset over the full detector dynamic range.

RMS power detector 100 has the advantage that it allows realization of awide dynamic range RMS-DC converter with high accuracy and temperaturestability. RMS power detector also has an disadvantage that, as VGA 102processes RF input signal 101, VGA 102 requires a large bandwidth overthe full VGA gain range (e.g., at least equal to the required detectordynamic range in dB). Another disadvantage of RMS power detector 100 isthat its attainable bandwidth is primarily limited by the bandwidth ofthe VGA. The maximum operating frequency of RMS power detector 100 isthus associated with the bandwidth of the VGA, which in turn increaseswith the bipolar transition frequency f_(T).

Another approach to extend dynamic range uses low-frequency feedback incombination with two square cells, as depicted in FIG. 2. As shown inFIG. 2, first square cell 207 a is driven by high-frequency input signal201, while second square cell 207 b is driven by a DC signal, which isderived by feedback control circuit 209 from detector output signal 204.Feedback control circuit 209 has a (non-linear) transfer function thatdetermines the overall transfer of the power detector. At sufficientlyhigh loop gain, the feedback loop equalizes the output signals 205 a and205 b of square cells 207 a and 207 b, respectively. The difference 206of output signals 205 a and 205 b is integrated by integrator 208 toprovide output signal 204 of RMS power detector 200. For a high loopgain, the overall transfer of the detector—from RF input power to DCoutput voltage—becomes equal to the inverse of feedback transfer 209.

RMS power detector 200 has similar characteristics to the RMS powerdetector described above that compresses the dynamic range of the squarecell output signal using a circuit with a non-linear transfer function.Again, only a single square cell need to operate at high frequencies,thus enabling a high RMS power detector bandwidth to be achieved.Another advantage is the matching of temperature drift and deviceoffsets, so as to improve the accuracy and dynamic range. Theseadvantages are compared to those achieved for the RMS power detectorthat compresses the dynamic range. The disadvantages of RMS powerdetector 200 includes (a) requiring both large device sizes and trimmingof the square cells to achieve a reasonable dynamic range, therebyundesirably reducing the attainable bandwidth; (b) the feedback looptypically results in a slow detector response (i.e., a lengthy responsetime), and (c) potential instability since the loop gain variessignificantly as a function of the input power level applied to thedetector

Yet another bandwidth extension technique uses linear analog multipliersto carry out the squaring operations, and applies chopping to eliminatedevice offsets generated inside the multipliers. This technique isdiscussed in Kouwenhoven and U.S. Pat. No. 7,197,292. The analogmultipliers can implement chopping, which is a much more effective wayfor reducing offsets in a square cell than both device scaling andtrimming, and potentially allows higher detector operating frequencies.A multiplier-based square cell, however, has a considerably lowerbandwidth than other square cells and is therefore less suited torealize an RMS-DC converter at very high frequencies. Also, amultiplier-based square cell operates at much higher current densitiesand results in higher overall power consumption.

SUMMARY

The present invention provides an RMS-DC converter architecture thatuses chopping around—intrinsically high-bandwidth—square cells toeliminate offset, thus enabling high-bandwidth operation because (a)only a small portion of the circuitry (i.e., a single square cell)operates at high frequencies; (b) high-bandwidth square cells may beused; and (c) chopping minimizes the required device size to achieve anacceptable square cell dynamic range, thereby maximizing the square cellbandwidth. In addition, an RMS-DC converter according to the presentinvention consumes less power than conventional RMS converter of theprior art that requires a high-frequency variable gain amplifier.

In accordance with one embodiment of the present invention, an RMS to DCconverter applies chopping to a combination of two square cells so as toeliminate DC offset from the square cells' output signals. The RMS to DCconverter of the present invention may include a first input switch forreceiving an input signal supplied to the RMS to DC converter, andtransferring the input signal alternatively to a first square cell or toa second square cell, but not to both simultaneously. A second inputswitch may receive a reference signal and transfer it alternately to thesecond square cell or to the first square cell, but not to bothsimultaneously. The first and second input switches are controlled so asto provide the first square cell with the input signal, when the secondsquare cell is supplied with the reference signal, and to supply thefirst square cell with the reference signal, when the second square cellis provided with the input signal. A subtraction operation may beperformed to provide a difference signal representing a differencebetween the output signals of the first and second square cells. Theoutput signals may be filtered either before or after the subtractionoperation, or both, to eliminate high-frequency components.

In one embodiment of the present invention, an output switch may beprovided to change the polarity of the difference signal. A clock signalmay control the states of the input switches and the output switch. Theswitches may be controlled at the same frequency, but a phase differencemay exist between the control signals applied to the input switches andthe control signal applied to the output switch—different combinationsof clock signals can be applied to both switches.

In accordance with another embodiment of the present invention, thereference signal may be a DC signal, e.g. zero. The reference signal mayalso be a wave-shaped signal, and the chopped square cell determines thedifference between the average power levels of the input signal and thereference signal.

In accordance with another embodiment of the present invention an RMS toDC converter may comprise a chopped square cell configuration, in whichthe first square cell receives an input signal supplied to the RMS to DCconverter, and the second square cell receives a reference signalproduced by a feedback circuit coupled to the output terminal of the RMSto DC converter. An output amplifier may provide an output signalresponsive to the averaged difference between output signals of thesquare cells. The output amplifier may provide the output signal of theRMS to DC converter. The output amplifier may include a number of gainamplifier stages, one or more of which may have a variable gainadjustable in accordance with an adjustment signal. The feedback circuitmay produce a DC or AC feedback signal derived from the output signal ofthe RMS to DC converter. The feedback signal may be supplied to theinput of the second square cell. Also, the feedback circuit may producean additional signal applied to control the gain of one or more gainamplifiers in the output amplifier.

In accordance with one embodiment of the present invention, the switchcontrol signal (i.e. the chopper signal) may have a frequency that isless than the lowest frequency of the input signal. The frequency of theswitch control signal may also be lower than the bandwidth of the inputsignal, (i.e. lower than the difference between the highest and thelowest frequencies of the input signal). The conversion technique of thepresent invention may improve performance of an RMS to DC converter byextending the dynamic range of the RMS to DC converter at a givenoperating frequency. Alternatively, the conversion technique of thepresent invention may extend useable operating frequency range of an RMSto DC converter while maintaining an acceptable dynamic range.

Offset chopping may be applied to a square cell, thereby enhancing theuseful dynamic range for a given transistor size.

The present invention is better understood upon consideration of thedetailed description below in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an RMS-DC converter 100 which extends its dynamic range byplacing variable gain amplifier (VGA) 102 at the input terminal ofsquare cell 107.

FIG. 2 shows RMS power detector 200, in which low frequency feedback isused in conjunction with square cells 207 a and 207 b.

FIG. 3 illustrates chopper-stabilized square cell 300, in accordancewith one embodiment of the present invention.

FIGS. 4( a) to 4(h) show the waveforms of various signals inchopper-stabilized square cell 300 of FIG. 3, when reference signal 302is the ground reference (i.e., zero volts).

FIGS. 5( a) to 5(g) show the spectra of various signals obtained bysimulation of chopper-stabilized square cell 300 of FIG. 3 at a chopperfrequency of 0 Hz.

FIGS. 6( a) to 6(g) show the spectra of various signals obtained bysimulation of chopper-stabilized square cell 300 of FIG. 3 at a chopperfrequency of 20 MHz.

FIGS. 7( a) and 7(b) show the output spectra of the output signal ofswitch 305 a, when chopper clock signal 310 is a square wave and whenchopper clock signal 310 is sinusoidal, respectively.

FIGS. 8( a) and 8(b) show the spectra of the input signal of switch 305a without a DC blocking capacitor and with the DC blocking capacitor,respectively.

FIGS. 9( a) to 9(g) show the spectra of various signals obtained bysimulation of chopper-stabilized square cell 300 of FIG. 3 at a chopperfrequency of 1 MHz.

FIG. 10 illustrate the output spectra of the output signal of squarecell 307 a for both a 1 MHz chopper clock frequency (dark) and a 20 MHzchopper clock frequency (light).

FIG. 11 shows the response of square cell 307 a for a 1-tone and 9-toneinput signal (same average power) at chopper frequencies of 1 MHz and 20MHz.

FIG. 12 illustrates the effectiveness of the choppers in eliminating DCoffset from the square cell transfer function.

FIGS. 13( a) and 13(b) show current and voltage switches, respectively,that are suitable for implementing any of switches 308 a, 308 b, 305 aand 305 b.

FIGS. 14( a) and 14(b) show square cell topologies that are suitable foruse in the chopped square cell driven single-ended and differentially,respectively.

FIG. 15 shows RMS-DC converter 400 based on the chopper stabilizedsquare cells, in accordance with one embodiment of the presentinvention.

FIG. 16 shows variable gain amplifier 500 suitable for implementingvariable gain amplifier 404.

FIG. 17 shows the transfer function of RMS-DC converter 400, plotted asthe voltage of output signal 412 versus RMS power of input signal 411.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 3 illustrates chopper-stabilized square cell 300, in accordancewith one embodiment of the present invention. As shown in FIG. 3,chopper-stabilized square cell 300 includes input signal 301 andreference signal 302, which are each selectively provided by eitherswitches 308 a or 308 b to square cell 307 a or square cell 307 b,depending on the state of switches 308 a and 308 b. At any given time,if switch 308 a is set to receive input signal 301, switch 308 b is setto receive reference signal 302. Alternatively, if switch 308 a is setto receive reference signal 302, switch 308 b is set to receive inputsignal 301. As each square cell has internal offsets that add to eitherthe input signal or the output signal, these offsets are represented byadders 303 a and 303 b that add offsets X_(OS1) and X_(OS2) to thesignals provided to square cells 307 a and 307 b, respectively, andadders 304 a and 304 b that add offsets Y_(OS1) and Y_(OS2) to theoutput signals of square cells 307 a and 307 b, respectively. The outputoffset-adjusted output signals of square cells 307 a and 307 b areprovided by switches 305 a and 305 b to difference circuit 309, whichprovides their difference as output signal 306 for chopper-stabilizedsquare cell 300. The offset components X_(OS1), X_(OS2) and Y_(OS1),Y_(OS2) are uncorrelated and are each often large relative to outputsignal 306. Chopper-stabilized square cell 300 represents a balancedsquare cell that has an RF input and a reference input and whichachieves a zero output signal for a zero input signal. Square cells thatdo not apply chopping according to the present invention have a limiteddynamic range that is typically 20-30 dB.

Each of switches 305 a, 305 b, 308 a and 308 b may be implemented asvoltage switches (e.g. using MOS-transistors in triode), or as currentswitches (e.g., using bipolar or MOS differential pairs). Currentswitches may provide a higher bandwidth, but typically require an inputamplifier to convert a high-frequency input voltage into an inputcurrent. FIGS. 13( a) and 13(b) show current and voltage switches,respectively, that are suitable for implementing any of switches 308 a,308 b, 305 a and 305 b. FIGS. 14( a) and 14(b) illustrate, respectively,single-ended and differential square cells suitable for implementingsquare cells 307 a and 307 b. The chopper operation allows asimplification of the square cell topology (i.e., the DC referencecurrent needed to achieve zero output current at zero input voltage isnot required).

Chopping is a technique that reduces offset in amplifiers, for example.In chopping, the input signal is typically up-converted beforeamplification to an intermediate frequency (IF) that is higher than thehighest frequency in the input signal, and then down-converted back tothe original frequency. Any DC offset introduced in the amplifier isup-converted by the same operation that realizes the down-conversion ofthe amplified input signal. High-frequency ripple caused by theup-converted offset are eliminated by low-pass filtering. Up-conversionand down-conversion can be achieved simply changing the polarity of theinput signal in accordance with the chopper frequency. In a square cell,this approach does not work, as the squaring operation rectifies theinput signal—eliminating the polarity inversions—and thus produces anoutput signal component at DC, where the offset to be eliminated alsoresides. In order to achieve an output signal component at IF, ratherthan at DC, the square cell input signal is switched on and off at thechopper frequency.

The input chopper of FIG. 3, i.e., switches 308 a and 308 b, alternatesthe RF input signal and input reference signal between square cells 307a and 307 b. Under this arrangement, when square cell 307 a receives RFinput signal 301, square cell 307 b receives the reference signal 302,and when square cell 307 b receives RF input signal 301, square cell 307a receives the reference signal 302. FIGS. 4( a) to 4(h) illustrate thewaveforms of various signals in the square cell 300 of FIG. 3. FIG. 4(a) shows RF input signal 301. For simplicity, reference signal 302 isset equal to zero volts (i.e., ground reference) in FIG. 4. Chopperclock signal 310 with controls switches 308 a, 308 b, 305 a and 305 b isshown in FIG. 4( b). The output signals of switches 308 a and 308 b areshown in FIGS. 4( c) and 4(d), respectively. FIGS. 4( e) and 4(f) showthe signals at switches 305 a and 305 b, respectively, after thesquaring operations square cells 307 a and 307 b and including theoffsets. FIG. 4( g) shows the difference between the input signalsapplied to switches 305 a and 305 b respectively. FIG. 4( h) shows theoutput signal of difference circuit 309. The difference of the outputsignals of square cells 307 a and 307 b has a component that isproportional to the squared result of RF input signal 301, modulated onchopper clock signal 310 (i.e. at a non-zero IF), while the offsetintroduced by square cells 307 a and 307 b are located at DC. Thus,after the second chopper (i.e., switches 305 a and 305 b), the squaredsignal is down-converted to DC, while the offsets are up-converted bythe chopper clock. There are, therefore, two different ways to eliminatethe offset. The first way passes a difference of the square cell outputsignals—prior to the second chopper operation—through a high-passfilter, eliminating the DC offsets while preserving the up-convertedsignal components. The second way passes an output signal of the secondchopper circuit through a low pass filter, thereby suppressing theup-converted offset while passing the down-converted output signal.These approaches may be combined to achieve better offset suppression.

The output signal of the input chopper (i.e., switches 308 a and 308 b)may contain a component at the chopper frequency that is notproportional to the input signal due to, for example, charge injectionin the input switches, or a DC component in the input signal of thechopper. Such components are down-converted by the second chopper (i.e.,switches 305 a and 305 b) and introduce a dynamic offset in the outputsignal that compromises the dynamic range of the chopper-stabilizedsquare cell. These components may be reduced, for example, by ensuringthat the input signal is AC coupled to the input square cell.Alternatively, these components may also be reduced by choosing achopper frequency that is much lower than the input signal frequency.Under this second way, the direct feed-through can then be eliminatedusing a high-pass filter of the chopper output signal, therebysuppressing the signal at the chopper frequency, but passing signalswithin the input frequency plus or minus the chopper frequency. Thisapproach may be implemented in power detectors. A third approach toreducing these components at output terminals of the first choppers(e.g., switches 308 a and 308 b) is to choose a chopper frequency thatis as low as possible, so as to minimize charge injection effects.

A duty cycle different from 50% can cause a residual offset component inthe output signal of the chopper-stabilized square cell; if the chopperclock signal has a DC component, not all DC offset components areup-converted to the chopper frequency by the output chopper. Adivide-by-2 circuit can provide an effective solution to maintain the50% duty cycle.

Clock signals with a finite slew-rate may cause the chopper switches topass slowly through their linear operating region, thus allowing DCoffsets to pass through the switches during a portion of the clockcycle. This effect can be eliminated by applying non-overlapping clocksto the output switches (i.e., break-before-make), which ensures that noDC path to the output exists at any instant during the clock cycle. Theswitches may be controlled at the same frequency, but a phase differencemay exist between the control signals applied to the input switches andthe control signal applied to the output switch—different combinationsof clock signals can be applied to both switches, as illustrated in thearticle, “Chopper Stabilization of Analog Multipliers, Variable GainAmplifiers, and Mixers,” by Godoy et al., published in the IEEE Journalof Solid Slate Circuits, vol. 43, No. 10, October 2008, pp. 2311-2321.

Simulations based on idealized Verilog models of the square cells andswitches have been used to validate the relationships derivedpreviously. In these simulations, which cover chopper frequencies at 0Hz, 20 MHz and 1 MHz, the input signal frequency was chosen to be aninteger multiple of the simulated chopper frequency (e.g., the inputsignal frequency is selected to be f_(in)=100 MHz), except for the casewhere the chopper frequency is 0 Hz. However, it should be noted that aninteger relationship is not required between the chopper frequency andthe input frequency for correct chopped square cell operation. The inputsignal has also a selected bandwidth of 8 MHz. The equivalent inputoffset in square cell 307 a was chosen to be 10 mV, and zero mV insquare cell 307 b. An output offset current of 10 μA was added at outputterminal of square cell 307 a. The DC offset component in the inputsignal to the second chopper (i.e., switch 305 a) is suppressed by a DCblocking capacitor. The conversion gains of square cells 307 a and 307 bare each 300 μA/V² are terminated into 10 kΩ.

FIGS. 5( a) to 5(g) show the spectra of various signals obtained bysimulation of chopper-stabilized square cell 300 of FIG. 3 at a chopperfrequency of 0 Hz. FIG. 5( a) show the spectrum of RF input signal 301.FIG. 5( b) show the spectrum of the output signal of switch 308 a; atf_(chop)=0 Hz, this spectrum is the same as the spectrum for RF inputsignal 301 shown in FIG. 5( a). FIG. 5( c) shows the spectrum of inputsignal X₁ at the input terminal of square cell 307 a, which includesinput offset X_(OS1) represented by an impulse at 0 Hz. FIG. 5( d) showsthe spectrum of the output signal at the output terminal of square cell307 a, which represent the convolution of the spectra of RF input signal301 and input offset X_(OS1) with itself. As expected, this spectrum haspeaks around f=0 (desired component), f=f_(RF) (cross-term betweensignal and offset) and f=2f_(RF) (double frequency term due to thesquaring operation). FIG. 5( e) show the spectrum of the output signalat square cell 307 a, including an additional output current offsetY_(OS1), which adds an impulse at f=0 that cannot be separated from theinput signal. FIG. 5( f) shows the spectrum of the output signal at theoutput terminal of switch 305 a; at f_(chop)=0 Hz, this spectrum is thesame as the spectrum in FIG. 5( e). FIG. 5( g) shows the spectrum ofoutput signal 305, after low-pass filtering. This reference simulationshows that the output DC offset Y_(OS1) only contributes at DC, whilethe equivalent input offset X_(OS1) also has a contribution around atf_(RF) (the frequency of RF input signal 301) due to cross-terms.

FIGS. 6( a) to 6(g) show the spectra of various signals obtained bysimulation of chopper-stabilized square cell 300 of FIG. 3 at a chopperfrequency of 20 MHz, which is much higher than the bandwidth of RF inputsignal 301. FIG. 6( a) show the spectrum of RF input signal 301. FIG. 6(b) show the spectrum of the output signal of switch 308 a. FIG. 6( c)shows the spectrum of input signal X₁ at the input terminal of squarecell 307 a, which includes input offset X_(OS1) represented by animpulse at 0 Hz. FIG. 6( c) shows a spectrum that contains side-bands atω_(i)±nω_(i), where ω_(i) is the center frequency of RF input signal 301(100 MHz) and ω_(c) is the chopper frequency (20 MHz). Since a squarewave was used for the chopper, only odd harmonics are present. Becausethe choppers are turned on and off (rather than the output signalpolarity being changed), the DC component in the output signal of theinput choppers provides the component at the input signal frequency (100MHz). Table 1 summarizes the various components of the spectrum of FIG.6( c):

TABLE 1 Lower side-band Upper side-band Chopper Signal Harmonicsfrequency (MHz) frequency (MHz) 0 100 100 1 80 120 3 40 160 5 0 200 7−40 240 2n + 1 f_(RF) − (2n + 1)f_(chop) f_(RF) + (2n + 1)f_(chop)

FIG. 6( d) shows the spectrum of the output signal at the outputterminal of square cell 307 a, which represent the convolution of thespectra of RF input signal 301 and input offset X_(OS1) with itself andeach other before output DC offset Y_(OS1) is added. The side-bands ofthe signal components are twice as wide as the input spectrum shown inFIG. 6( c), due to the squaring operation in square cell 307 a, and arecentered at the odd harmonics of the chopper frequency. Table 2summarizes the various side band components in the output spectrum ofsquare cells 307 a and 307 b depicted in FIG. 6( d), relative to thecomponents found when no chopping is applied (0 Hz). Without chopping,the square cell output spectrum would have components at 0 Hz and at 2×the input frequency (2f_(RF)) of the

TABLE 2 Chopper Signal Side bands of Side bands of Component HarmonicsComponent at f = 0 (MHz) at f = 2 f_(RF) (MHz) 1 20 180 220 3 60 140 2605 100 100 300 7 140 60 340 9 180 20 380 2n + 1 (2n + 1)f_(chop) 2f_(RF)− 2f_(RF) + (2n + 1)f_(chop) (2n + 1)f_(chop)

The signal components are located at the odd harmonics of the chopperfrequency, thus separated by 2*fchop=40 MHz. In this particular case,the two signal side-bands—one that would be located at 0 Hz withoutchopping and the other at the second harmonic of RF input signal301—align, because their separation of 2*f_(RF)=200 MHz is an integermultiple of the side-band separation 2*fchop=40 MHz.

The side-bands corresponding to the cross-terms between RF input signal301 and input offset X_(OS1) are located at the odd harmonics of thechopper frequency, centered at the center frequency of RF input signal301, as shown in Table 3. The side-bands are copies of the spectrum ofRF input signal 301, scaled by the magnitude of output offset Y_(OS1).

TABLE 3 Lower side-band Upper side-band Chopper Signal Harmonicsfrequency (MHz) frequency (MHz) 1 80 120 3 40 160 5 0 200 7 −40 240 2n +1 f_(RF) − (2n + 1)f_(chop) f_(RF) + (2n + 1)f_(chop)

In this simulation, the center frequency of RF input signal, thecross-product of RF input signal 301 and input offset X_(OS1) coincidewith the even harmonics of the chopper frequency. It is thus desirablethat the center frequency of RF input signal 301 is considerably higherthan the chopper frequency; this will significantly reduce the magnitudeof any cross-product terms that land at the primary signal component (atfchop=20 MHz).

FIG. 6( e) show the spectrum of the output signal at square cell 307 a,including an additional output current offset Y_(OS1). FIG. 6( f) showsthe spectrum of the output signal at the output terminal of switch 305a. Ideally, the signal spectrum of FIG. 6( f) only has components at DCand not at higher harmonics of RF input signal 301. However, if thechopper signal is not ideally square, some higher harmonic componentswould remain present. Table 4 shows the signal components of the outputsignal at switch 305 a:

TABLE 4 Chopper Signal Side bands of Component Side bands of ComponentHarmonics at f = 0 (MHz) at f = 2 f_(RF) (MHz) 0 0 200 200 2 40 160 2404 80 120 280 6 120 80 320 8 160 40 360 10  200 0 400 2n 2nf_(chop)2f_(RF) − 2nf_(chop) 2f_(RF) + 2nf_(chop)

FIG. 6( g) shows the spectrum of output signal 305, after low-passfiltering. FIGS. 7( a) and 7(b) show the output spectra of the outputsignal of switch 305 a, when chopper clock signal 310 is a square waveand when chopper clock signal 310 is sinusoidal, respectively; thehigher harmonics of RF input signal 301 diminish when the chopper signalapproaches a square wave. As shown in FIG. 7( b), a strong signal sideband around the second harmonic of the chopper frequency is present(only 3 dB below the side-band at DC) in the sinusoidal case. As shownin FIG. 7( a), the side band around the second harmonic of the chopperfrequency (40 MHz) is largely suppressed (by almost 68 dB) in the squarewave case.

As explained above, the DC offset component in the input signal to thesecond chopper (i.e., switch 305 a) is suppressed by a DC blockingcapacitor. FIGS. 8( a) and 8(b) show the spectra of the input signal ofswitch 305 a without a DC blocking capacitor and with the DC blockingcapacitor, respectively. As shown in FIG. 8( a) the offsets cause largespikes at the harmonics of the chopper frequency, resulting insignificant ripples. The DC blocking capacitor helps to reduce theseripples.

FIGS. 9( a) to 9(g) show the spectra of various signals obtained bysimulation of chopper-stabilized square cell 300 of FIG. 3 at a chopperfrequency of 1 MHz. FIG. 9( a) show the spectrum of RF input signal 301.FIG. 9( b) show the spectrum of the output signal of switch 308 a. FIG.9( c) shows the spectrum of input signal X₁ at the input terminal ofsquare cell 307 a, which includes input offset X_(OS1) represented by animpulse at 0 Hz. As shown in FIG. 9( c), the side-bands of chopped RFinput signal 301 are aliasing with RF input signal 301, resulting in—ona logarithmic scale—an almost triangular shaped input spectrum. FIG. 9(d) shows the spectrum of the output signal at the output terminal ofsquare cell 307 a. As shown in FIG. 9( d), a copy of the output signalis seen centered at f=100 MHz, which is shifted to DC by the secondchopper operation (i.e., by the actions of switches 305 a and 305 b).

FIG. 9( e) show the spectrum of the output signal at square cell 307 a,including an additional output current offset Y_(OS1), which adds animpulse at f=0. FIG. 9( f) shows the spectrum of the output signal atthe output terminal of switch 305 a. FIG. 9( g) shows the spectrum ofoutput signal 305, after low-pass filtering.

FIG. 10 illustrates the output spectra of the output signal of squarecell 307 a for both a 1 MHz chopper clock frequency (dark) and a 20 MHzchopper clock frequency (light). In both cases the same signal spectrumis reproduced around DC. With a 1 MHz clock, more side bands are visiblein the same bandwidth as with the 20 MHz clock (in fact, 20 times asmany).

FIG. 11 shows the response of square cell 307 a for a 1-tone and 9-toneinput signal (same average power) at chopper frequencies of 1 MHz and 20MHz. The responses are virtually the same, despite the very differentfrequency spectra, as seen from corresponding FIGS. 6( a) to 6(g) and9(a) to 9(g).

FIG. 12 illustrates the effectiveness of the choppers in eliminating DCoffset from the square cell transfer function. An input offset voltageof 5 mV and output offset current of 10 μA was inserted in a Verilog-Amodel of a chopper-stabilized square cell. When the chopper is turnedoff (light), the offsets completely saturate the square cell output,leaving virtually no useful square cell dynamic range. With the chopperis turned on (dark), the offset is completely removed from the outputsignal.

FIG. 15 shows RMS-DC converter 400 based on the chopper stabilizedsquare cells, in accordance with one embodiment of the presentinvention. As shown in FIG. 15, square cells 403 a and 403 b are choppedby switch networks 402 and 405 based on the principles described abovewith respect to chopper-stabilized square cell 300 of FIG. 3. In FIG.15, RMS-DC converter 400's output signal 412 is provided to feedbackcircuit 407, which provides control signal 413 to reference inputterminal of chopper-stabilized square cell 403 a at switch network 402.Control signal 413 performs the same function as input reference signal302 of FIG. 3. Control signal 413 may be a DC or AC signal derived fromoutput signal 412. As shown in FIG. 15, feedback circuit 407 may providecontrol signal 414, which controls the gain of a variable gain amplifier404 in the forward path. The inclusion of a variable gain amplifier 404is not required, but helps to maintain a substantially constantloop-gain in RMS-DC converter 400 over the full operating power range.FIG. 16 shows variable gain amplifier 500 suitable for implementingvariable gain amplifier 404. In steady state, the average output signalof square cells 403 a and 403 b are equal, such that the overalltransfer from RMS input signal 411 to DC output signal 412 approachesthe inverse of the transfer function of feedback circuit 407. FIG. 17shows the transfer function of RMS-DC converter 400, plotted as thevoltage of output signal 412 versus RMS power of input signal 411.

The above detailed description is provided to illustrate the specificembodiments of the present invention and is not intended to be limiting.Numerous variations and modifications within the scope of the presentinvention are possible. The present invention is set forth in theaccompanying claims.

I claim:
 1. A chopper stabilized square cell receiving a first signal, asecond signal and a clock signal, and having a first output signal and asecond output signal, comprising: a first square cell; a second squarecell, wherein the first and second square cells each receive an inputsignal and provide an output signal; an input switch circuit operated bythe clock signal to provide the first signal and the second signal in analternating manner to the first square cell and the second square cell,such that when the first signal is provided as the input signal to thefirst square cell, the second signal is provided as the input signal tothe second square cell and when the first signal is provided as theinput signal to the second square cell, the second signal is provided asinput signal to the first square cell; and an output switch circuitoperated by the clock signal to provide the output signal of the firstsquare cell and the output signal of the second square cell in analternating manner as the first output signal and the second outputsignal, such that when the output signal of the first square cell isprovided as the first output signal, the output signal of the secondsquare cell is provided as the second output signal and when the outputsignal of the first square cell is provided as the second output signal,the output signal of the second square cell is provided as the firstoutput signal.
 2. The chopper-stabilized square cell of claim 1, furthercomprising a difference circuit receiving the first and second outputsignals to provide an output signal representing a difference betweenthe first and second output signals.
 3. The chopper-stabilized squarecell of claim 2, further comprising a low pass filter operating on theoutput signal of the difference circuit.
 4. The chopper-stabilizedsquare cell of claim 1, further comprising a first high pass filteroperating on the first output signal and a second high pass filteroperating on the second output signal.
 5. The chopper-stabilized squarecell of claim 1, wherein the input switch circuit comprises a firstswitch and a second switch.
 6. The chopper-stabilized square cell ofclaim 1, wherein the clock signal comprises a sinusoidal signal.
 7. Thechopper-stabilized square cell of claim 1, wherein the clock signalcomprises a square wave.
 8. The chopper-stabilized square cell of claim1, wherein the input switch circuit and the output switch circuitoperate by different phases of the clock signal.
 9. Thechopper-stabilized square cell of claim 1, wherein the second signalcomprises a DC reference signal.
 10. The chopper-stabilized square cellof claim 1, wherein the second signal comprises a signal of apredetermined waveform and power.
 11. The chopper-stabilized square cellof claim 1, wherein the clock signal has a frequency lower thanfrequencies of the first signal.
 12. The chopper-stabilized square cellof claim 1, wherein the clock signal has a frequency lower than abandwidth of the first signal.
 13. The chopper-stabilized square cell ofclaim 1, wherein a center frequency of the first signal is an integralmultiple of a frequency of the clock signal.